Ta có :
\(B=\dfrac{1}{4}+\dfrac{1}{5}+\dfrac{1}{6}+...........+\dfrac{1}{19}\)
\(B=\dfrac{1}{4}+\left(\dfrac{1}{5}+\dfrac{1}{6}+......+\dfrac{1}{9}\right)+\left(\dfrac{1}{10}+\dfrac{1}{11}+..........+\dfrac{1}{19}\right)\)
Ta thấy :
\(\dfrac{1}{5}+\dfrac{1}{6}+\dfrac{1}{7}+\dfrac{1}{8}+\dfrac{1}{9}>\dfrac{1}{9}+\dfrac{1}{9}+\dfrac{1}{9}+\dfrac{1}{9}+\dfrac{1}{9}\)\(=\dfrac{1}{9}.5=\dfrac{5}{9}\)\(>\dfrac{1}{2}\)
\(\dfrac{1}{10}+\dfrac{1}{11}+\dfrac{1}{12}+......+\dfrac{1}{19}>\dfrac{1}{19}+\dfrac{1}{19}+.........+\dfrac{1}{19}\)\(=\dfrac{1}{19}.5=\dfrac{5}{19}\)\(>\dfrac{1}{2}\)
\(\Rightarrow B>\dfrac{1}{4}+\dfrac{1}{2}+\dfrac{1}{2}=\dfrac{5}{4}>1\)
\(\Rightarrow B>1\rightarrowđpcm\)
~ Chúc bn học tốt ~
